Percent Decrease Formula - Derivation, Examples (2024)

Percent decrease refers to the percentage change in the value when it is decreased over a period of time. For example, a decrease in the level of rainfall, a decrease in the number of Covid patients, etc. Percent decrease can be calculated by using the percent decrease formula. In this section, we will be discussing the percent decrease formula. Let us learn the percent decrease formula with a few solved examples.

What is Percent Decrease Formula?

The percent decrease formula gives the decrease in quantity with respect to its initial value. To calculate the decrease in percentage, we first need to find the difference in the values. Then, divide the difference by the initial value and multiply it by 100. The percent decrease formula is given as:

Percent Decrease = [(Old Value - New Value) / Old Value] × 100]

Percent Decrease Formula

There are two simple steps to calculate the percent decrease using the percent decrease formula, they are:

• Step 1: Find out the difference between the numbers, i.e., Decrease = Old value - New value
• Step 2: Divide the decrease by the old value and multiply it by 100. This makes the percent decrease formula, Percent Decrease = [(Old Value - New Value) / Old Value] × 100]

Percentage Increase and Decrease

Percentage increase and decrease is the percentage change in the value. Percentage change is the difference between the new value and the old value that is given. In order to find the percentage change, this difference is divided by the old value and multiplied by 100 to get the percentage increase or decrease.

Now, it should be noted that when the new value is more than the old value, then it is a percentage increase. For example, if the price of a book changes from $5 to $8, there is an increase in the price. Whereas, when the old value is greater than the new value, in that case, it is a percentage decrease. For example, if the price of a table changes from $10 to $8, there is a decrease in the price.

Examples Using Percent Decrease Formula

Example 1: The number 53 is misread as 35. Find the percent decrease using the percent decrease formula.

Solution:

Here, new value = $35 and old value = $53

Using the Percent decrease formula, we get

Percent Decrease = [(Old Value - New Value) / Old Value] × 100

= [(53 - 35)/53] × 100

= 18/53 × 100

= 33.9%

Therefore, the percent decrease of the number is approximately 34%

Example 2: An article whose CP is $250 was sold for $230. Use the percent decrease formula to find the percent decrease in the price of the article.

Solution:

Here, new value = $230 and old value = $250

Using the Percent decrease formula, we get

Percent Decrease = [(Old Value - New Value) / Old Value] × 100

= [(250 - 230)/250] × 100

= 20/250 × 100

= 8%

Therefore, the percentage decrease in the price of the article is 8%.

Example 3: A fruit seller used to sell strawberries for $80 per dozen. Now, he reduced the cost of a dozen strawberries by 5%. What is the price of a dozen strawberries now? Calculate by using the percent decrease formula.

Solution:

Let the new value for a dozen strawberries be x.

According to the percent decrease formula,

Percent Decrease = [(Old Value - New Value) / Old Value] × 100

It is given that percent decrease = 5%; New value = x, old value = 80

So, putting these values in the equation,

5 = [(80 – x)/80] × 100

x = 76

So, the new price of a dozen of strawberries is $76.